Railroad is a commonly used transportation system on Earth, and it can be used on Mars as well. Iron ,the main construction material, is abundant on the Martian surface. Compared with most other transportation systems, the railroad is basically lo-tech and can, therefore, be maintained with low effort.
Compared with rovers a railroad system is rather inflexible, but it can have an advantage for frequently used ways. On the long run it allows energy optimized transport. No batteries or fuels are necessary if electrical engines and power lines are used. Especially for driver-less material transport, it can be a central part of the settlement's infrastructure.
Elon Musk's initiative to develop the hyperloop technology allows the anticipation of a very similar transportation system on Mars. Compared to the terrestrial concept it would require only a thin-walled tube. The air pressure in the tube would be slightly higher than the surrounding Martian atmosphere, preventing the invasion of dust. Musk himself imagines a version without a tube on Mars.
Rolling equipment is subject to a number of forces, which together define the energy requirements of a rail system.
On Mars, the air resistance is negligible and can be discounted except at very high velocities.
Rolling friction should also be significantly lower on Mars. Friction is defined by the equation: F=uN. Where the friction factor (u) being a property of materials remains the same, but the vertical force (N) is reduced by the lower gravity. N is a force, and F=ma. Mass (m) is invariant from Earth to Mars, but the acceleration (a), is 38% of the acceleration on Earth. So trains will have less roll resistance and can be larger.
As on Earth, the rolling friction of a train should be significantly lower than the rolling friction of a truck. A significant amount of energy is also lost in truck tire walls as they flex and roll, which is less important for steel wheels.
Inertia of the train
The inertia of the train remains the same on Earth as on Mars. So the kinetic energy of the train, for the same velocity, will not be changed by the lower gravity. However, for electrical trains, regenerative braking could be used, returning to the grid when the train is stopped the energy that was required to accelerate the train up to speed. Regenerative braking may also be used to return to the grid the energy required to climb grades on Mars.
Steel rails would require 30-50 MJ/kg for their fabrication, according to the concepts on embodied energy. Considering rails with an average mass of 50 kg/m, one km of rail might mass 100 000 kg (100 tonnes) and require 5 000 000 MJ to fabricate. Supposing the Cost of energy on Mars to be about 150 $/GJ (in 2019 dollars), this represents a value of about 750 000$. To this we would need to add the cost of the ballast, the ties and of all the logistical support systems required.
The transport of a maintenance team
Peripheral parts of a Martian settlement might be several kilometers away from the living quarters. Energy generating stations (e.g. solar panels, wind turbines) are spread over a large area and have fixed positions. A lightweight railroad system might reduce the maintenance costs on the long run.
Transportation in tunnels
Parts of the colony will be underground. For mining activities, a railroad system provides a comfortable transportation of material and persons over long underground distances.
Connection between two settlements
Railroad covers both short and long distances. Even in the far future with more than one settlement on Mars, people will still be interested in efficient transportation systems. Only a magnetic levitation system might have a better energy balance.
Much of the cost of railroad construction lies in the cost of the infrastructure required to support the rails. Mars has interesting advantages as there are no swamps and essentially no soil, therefore it should be fairly simple to create a track way that is structurally sound without moving too much regolith around. However, this also applies to road construction, so the construction of roads on Mars should also be relatively cheap.
As the friction of the train will be less, the grades that a Martian railroad can climb may be less than on Earth. However, the trains will also have a lower weight, so the actual grades may be quite similar.
For the same mass, the weight on Mars will be less than on Earth, so the strain on the infrastructure should be less. Ballast might be less extensive, or the trains might be larger for the same quality of track and bed as on Earth.